FBI compare your name to the names of suspect terrorists after you submitted your I-485. You don't know when they finish the checking of your name because nobody will inform you of this. You need to send them emails to request the status of your name check, but they will not reply to your call immediately. I just got an email from FBI saying they finished my name check in January 2003 after I sent them emails twice in November 2004. However, my I-485 has been approved two weeks ago. As you know, I am not a terrorist so far. Actually, most of terrorists don't need green cards.